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Skewness-based projection pursuit: A computational approach

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  • Loperfido, Nicola

Abstract

Projection pursuit is a multivariate statistical technique aimed at finding interesting low-dimensional data projections by maximizing a measure of interestingness commonly known as projection index. Widespread use of projection pursuit has been hampered by the computational difficulties inherent to the maximization of the projection index. The problem is addressed within the framework of skewness-based projection pursuit, focused on data projections with highest third standardized cumulants. First, it is motivated the use of the right dominant singular vector of the third multivariate, standardized moment to start the maximization procedure. Second, it is proposed an iterative algorithm for skewness maximization which relies on the analytically tractable maximization of a third-order polynomial in two variables. Both visual inspection and formal testing based on simulated data clearly suggest that the asymptotic distribution of the maximal skewness achievable by a linear projection of normal data might be skew-normal. The potential of skewness-based projection pursuit for uncovering data structures is illustrated with Olympic decathlon data.

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  • Loperfido, Nicola, 2018. "Skewness-based projection pursuit: A computational approach," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 42-57.
    • Handle: RePEc:eee:csdana:v:120:y:2018:i:c:p:42-57
    DOI: 10.1016/j.csda.2017.11.001
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    10. Chunming Zhang & Jimin Ye & Xiaomei Wang, 2023. "A Computational Perspective on Projection Pursuit in High Dimensions: Feasible or Infeasible Feature Extraction," International Statistical Review, International Statistical Institute, vol. 91(1), pages 140-161, April.
    11. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
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    13. Shushi, Tomer, 2018. "A proof for the existence of multivariate singular generalized skew-elliptical density functions," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 50-55.
    14. Vincenzo Basile & Stefano Cervellera & Carlo Cusatelli & Massimiliano Giacalone, 2024. "Top–down disaggregation of life expectancy up to municipal areas, using linear self-regressive spatial models," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(4), pages 3703-3724, August.
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    17. Daniel A. Griffith, 2022. "Selected Payback Statistical Contributions to Matrix/Linear Algebra: Some Counterflowing Conceptualizations," Stats, MDPI, vol. 5(4), pages 1-16, November.

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